In many cases, a user population uses a shared computer system. However, there is a critical problem that frequently occurs in the early stages of the growth of the user population in a shared computer system that can only be accessed by authorized users who use the system to securely share information. Suppose that the number of users of the shared computer system is much smaller than the number of people on a selective list of eligible users and that a user may want to communicate with any other person on the selective list. Very frequently a user who wishes to collaborate with a person on the selective list will find that the person is not a user, and therefore cannot be sent information that would be securely shared on the shared computer system. This inability to communicate with a desired recipient severely limits the utility of the shared computer system. This is called the incomplete network problem, because while only a small fraction of the people on the selective list are users of the shared computer system, those users cannot use the shared computer system to connect with the majority of people on the selective list.
The incomplete network problem is further complicated by the need to maintain the shared computer system's security. A secure system ensures that only authorized users can access the system and the information that it stores, and that malicious parties cannot disrupt this access. On numerous recent occasions supposedly secure systems have been breached. Systems have been inappropriately accessed and sensitive data, such as financial and medical information, has been acquired by unauthorized people in many ways. These means have included hacking, insider defections, malicious software such as viruses, accidental data releases, and others. In addition, malicious parties have attacked and overwhelmed supposedly secure systems, such as the systems of some banks, thereby denying access to authorized users. These frequent and high-profile security violations, affecting a significant number of organizations, has given rise to increasing concern about computer and data security.
Therefore, there is a need to solve the incomplete network problem while maintaining all of the security properties of the shared computer system.